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This study presents an adaptively-refined quadtree grid method used in conjunction with a pressure-based flow solution algorithm for the incompressible Navier-Stokes equations. The quadtree grid, which is composed of quadrilateral cells that can be successively subdivided into four quadrants, is examined, and the quadtree data structure, and its advantages when used in the numerical solution of the Navier-Stokes equations, is discussed. Several strategies for solution adaptive grid refinement, which is used to resolve high-gradient flow regions, are then presented. Two different flow solution methods, the uni-dimensional power-law method and the upwind method, both based on a cell-centered, finite-volume technique, are studied. These methods solve the governing equations for the primitive variables on a colocated grid using the SIMPLE algorithm.